Advertisement

Pipette Aspiration of an Elastic Half-Space

  • Ivan Argatov
  • Gennady Mishuris
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 91)

Abstract

In this chapter, we consider the axisymmetric contact problem for a frictionless annular indenter and, in particular, solve this problem in the two limit situations of a narrow indenter and a wide indenter, depending on the ratio of the radii of the ring-shaped contact region. We then obtain the asymptotic solutions to the pipette aspiration problem in the two limiting cases.

References

  1. 1.
    Aleksandrov, V.M.: The axisymmetric problem of the action of a ring-shaped punch on an elastic half-space. Eng. J. Mech. Solids 4, 108–116 (1967) (in Russian)Google Scholar
  2. 2.
    Antipov, Y.A.: Analytic solution of mixed problems of mathematical physics with a change of boundary conditions over a ring. Mech. Solids 24, 49–56 (1989)Google Scholar
  3. 3.
    Argatov, I., Mishuris, G.: Pipette aspiration testing of soft tissues: the elastic half-space model revisited. Proc. R. Soc. A 472, 20160559 (18 pp) (2016)Google Scholar
  4. 4.
    Argatov, I.I., Nazarov, S.A.: The pressure of a narrow ring-shaped punch on an elastic half-space. J. Appl. Math. Mech. 60, 799–812 (1996)CrossRefGoogle Scholar
  5. 5.
    Barber, J.R.: Indentation of the semi-infinite elastic solid by a concave rigid punch. J. Elast. 6, 149–159 (1976)CrossRefGoogle Scholar
  6. 6.
    Borodachev, N.M.: On the nature of the contact stress singularities under an annular stamp. J. Appl. Math. Mech. 40, 347–352 (1976)CrossRefGoogle Scholar
  7. 7.
    Borodacheva, F.N.: Approximate method for determining the contact stresses under a ringshaped punch. Int. Appl. Mech. 15, 89–92 (1979)Google Scholar
  8. 8.
    Collins, W.D.: On the solution of some axisymmetric boundary value problems by means of integral equations. Proc. Edinb. Math. Soc. III(13), 235–246 (1963)CrossRefGoogle Scholar
  9. 9.
    Dhawan, G.K.: A transversely isotropic half-space indented by a flat annular rigid stamp. Acta Mech. 31, 291–299 (1979)CrossRefGoogle Scholar
  10. 10.
    Gladwell, G.M.L., Gupta, O.P.: On the approximate solution of elastic contact problems for a circular annulus. J. Elast. 9, 335–348 (1979)CrossRefGoogle Scholar
  11. 11.
    Grinberg, G.A., Kuritsyn, V.N.: Diffraction of a plane electromagnetic wave by an ideally conducting plane ring and the electrostatic problem for such a ring. Sov. Phys. 6, 743–749 (1962)Google Scholar
  12. 12.
    Gubenko, V.S., Mossakovskii, V.I.: Pressure of an axially symmetric circular die on an elastic half-space. J. Appl. Math. Mech. 24, 477–486 (1960)CrossRefGoogle Scholar
  13. 13.
    Hanson, M.T., Puja, I.W.: Love’s circular patch problem revisited closed form solutions for transverse isotropy and shear loading. Q. Appl. Math. 54(2), 359–384 (1996)CrossRefGoogle Scholar
  14. 14.
    Jahnke E., Emde F., Lösch F.: Special Functions: Formulae, Graphs, Tables, Nauka, Moscow (1977) (Russian transl.)Google Scholar
  15. 15.
    Jain, D.L., Kanwal, R.P.: Three-part boundary value problems in potential and generalised axially symmetric potential theories. J. Anal. Math. 25, 107–158 (1972)CrossRefGoogle Scholar
  16. 16.
    Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985)CrossRefGoogle Scholar
  17. 17.
    Love, A.E.H.: The stress produced in a semi-infinite solid by pressure on part of the boundary. Philos. Trans. Roy. Soc. Lond. Ser. A 228, 377–420 (1929)Google Scholar
  18. 18.
    Lur’e, A.I.: Three-dimensional Problems of Theory of Elasticity. Interscience, New York (1964)Google Scholar
  19. 19.
    Mossakovskii, V.I.: Estimating displacements in spatial contact problems. J. Appl. Math. Mech. (PMM) 15, 635–636 (1951) (in Russian)Google Scholar
  20. 20.
    Roitman, A., Shishkanova, S.: The solution of the annular punch problem with the aid of recursion relations. Sov. Appl. Mech. 9, 725–729 (1973)CrossRefGoogle Scholar
  21. 21.
    Shibuya, T., Koizumi, T., Nakahara, I.: An elastic contact problem for a half-space indented by a flat annular rigid stamp. Int. J. Eng. Sci. 12, 759–771 (1974)CrossRefGoogle Scholar
  22. 22.
    Sneddon, I.N.: Mixed Boundary Value Problems in Potential Theory. North-Holland, Amsterdam (1966)Google Scholar
  23. 23.
    Theret, D.P., Levesque, M.J., Sato, M., Nerem, R.M., Wheeler, L.T.: The application of a homogeneous half-space model in the analysis of endothelial cell micropipette measurements. J. Biomech. Eng. 110, 190–199 (1988)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of MechanicsTechnical University of BerlinBerlinGermany
  2. 2.Department of Mathematics, IMPACSAberystwyth UniversityAberystwythUK

Personalised recommendations